Introduction

MATLAB® and NumPy/SciPy have a lot in common. But there are many differences. NumPy and SciPy were created to do numerical and scientific computing in the most natural way with Python, not to be MATLAB® clones. This page is intended to be a place to collect wisdom about the differences, mostly for the purpose of helping proficient MATLAB® users become proficient NumPy and SciPy users. NumPyProConPage is another page for curious people who are thinking of adopting Python with NumPy and SciPy instead of MATLAB® and want to see a list of pros and cons.

Some Key Differences

In MATLAB®, the basic data type is a multidimensional array of double precision floating point numbers. Most expressions take such arrays and return such arrays. Operations on the 2-D instances of these arrays are designed to act more or less like matrix operations in linear algebra.

In NumPy the basic type is a multidimensional array. Operations on these arrays in all dimensionalities including 2D are elementwise operations. However, there is a special matrix type for doing linear algebra, which is just a subclass of the array class. Operations on matrix-class arrays are linear algebra operations.

MATLAB® uses 1 (one) based indexing. The initial element of a sequence is found using a(1). See note 'INDEXING'

Python uses 0 (zero) based indexing. The initial element of a sequence is found using a[0].

MATLAB®'s scripting language was created for doing linear algebra. The syntax for basic matrix operations is nice and clean, but the API for adding GUIs and making full-fledged applications is more or less an afterthought.

NumPy is based on Python, which was designed from the outset to be an excellent general-purpose programming language. While Matlab's syntax for some array manipulations is more compact than NumPy's, NumPy (by virtue of being an add-on to Python) can do many things that Matlab just cannot, for instance subclassing the main array type to do both array and matrix math cleanly.

In MATLAB®, arrays have pass-by-value semantics, with a lazy copy-on-write scheme to prevent actually creating copies until they are actually needed. Slice operations copy parts of the array.

In NumPy arrays have pass-by-reference semantics. Slice operations are views into an array.

In MATLAB®, every function must be in a file of the same name, and you can't define local functions in an ordinary script file or at the command-prompt (inlines are not real functions but macros, like in C).

NumPy code is Python code, so it has no such restrictions. You can define functions wherever you like.

MATLAB® has an active community and there is lots of code available for free. But the vitality of the community is limited by MATLAB®'s cost; your MATLAB® programs can be run by only a few.

NumPy/SciPy also has an active community, based right here on this web site! It is smaller, but it is growing very quickly. In contrast, Python programs can be redistributed and used freely. See Topical Software for a listing of free add-on application software, Mailing Lists for discussions, and the rest of this web site for additional community contributions. We encourage your participation!

MATLAB® has an extensive set of optional, domain-specific add-ons ('toolboxes') available for purchase, such as for signal processing, optimization, control systems, and the whole SimuLink® system for graphically creating dynamical system models.

There's no direct equivalent of this in the free software world currently, in terms of range and depth of the add-ons. However the list in Topical Software certainly shows a growing trend in that direction.

MATLAB® has a sophisticated 2-d and 3-d plotting system, with user interface widgets.

Addon software can be used with Numpy to make comparable plots to MATLAB®. Matplotlib is a mature 2-d plotting library that emulates the MATLAB® interface. PyQwt allows more robust and faster user interfaces than MATLAB®. And mlab, a "matlab-like" API based on Mayavi2, for 3D plotting of Numpy arrays. See the Topical Software page for more options, links, and details. There is, however, no definitive, all-in-one, easy-to-use, built-in plotting solution for 2-d and 3-d. This is an area where Numpy/Scipy could use some work.

MATLAB® provides a full development environment with command interaction window, integrated editor, and debugger.

Numpy does not have one standard IDE. However, the IPython environment provides a sophisticated command prompt with full completion, help, and debugging support, and interfaces with the Matplotlib library for plotting and the Emacs/XEmacs editors.

MATLAB® itself costs thousands of dollars if you're not a student. The source code to the main package is not available to ordinary users. You can neither isolate nor fix bugs and performance issues yourself, nor can you directly influence the direction of future development. (If you are really set on Matlab-like syntax, however, there is Octave, another numerical computing environment that allows the use of most Matlab syntax without modification.)

NumPy and SciPy are free (both beer and speech), whoever you are.

'array' or 'matrix'? Which should I use?

Short answer

Use arrays.

They are the standard vector/matrix/tensor type of numpy. Many numpy function return arrays, not matrices.

There is a clear distinction between element-wise operations and linear algebra operations.

You can have standard vectors or row/column vectors if you like.

The only disadvantage of using the array type is that you will have to use dot instead of * to multiply (reduce) two tensors (scalar product, matrix vector multiplication etc.).

Long answer

Numpy contains both an array class and a matrix class. The array class is intended to be a general-purpose n-dimensional array for many kinds of numerical computing, while matrix is intended to facilitate linear algebra computations specifically. In practice there are only a handful of key differences between the two.

Operator *, dot(), and multiply():

For array, '*' means element-wise multiplication, and the dot() function is used for matrix multiplication.

For matrix, '*' means matrix multiplication, and the multiply() function is used for element-wise multiplication.

Handling of vectors (rank-1 arrays)

For array, the vector shapes 1xN, Nx1, and N are all different things. Operations like A[:,1] return a rank-1 array of shape N, not a rank-2 of shape Nx1. Transpose on a rank-1 array does nothing.

You can treat rank-1 arrays as either row or column vectors. dot(A,v) treats v as a column vector, while dot(v,A) treats v as a row vector. This can save you having to type a lot of transposes.

Having to use the dot() function for matrix-multiply is messy -- dot(dot(A,B),C) vs. A*B*C.

Element-wise multiplication is easy: A*B.

array is the "default" NumPy type, so it gets the most testing, and is the type most likely to be returned by 3rd party code that uses NumPy.

Is quite at home handling data of any rank.

Closer in semantics to tensor algebra, if you are familiar with that.

All operations (*, /, +, ** etc.) are elementwise

matrix

Behavior is more like that of MATLAB® matrices.

Maximum of rank-2. To hold rank-3 data you need array or perhaps a Python list of matrix.

Minimum of rank-2. You cannot have vectors. They must be cast as single-column or single-row matrices.

Since array is the default in NumPy, some functions may return an array even if you give them a matrix as an argument. This shouldn't happen with NumPy functions (if it does it's a bug), but 3rd party code based on NumPy may not honor type preservation like NumPy does.

The use of operator overloading is a bit illogical: * does not work elementwise but / does.

The array is thus much more advisable to use, but in the end, you don't really have to choose one or the other. You can mix-and-match. You can use array for the bulk of your code, and switch over to matrix in the sections where you have nitty-gritty linear algebra with lots of matrix-matrix multiplications.

Facilities for Matrix Users

Numpy has some features that facilitate the use of the matrix type, which hopefully make things easier for Matlab converts.

mat has been changed to be a synonym for asmatrix, rather than matrix, thus making it concise way to convert an array to a matrix without copying the data.

Some top-level functions have been removed. For example numpy.rand() now needs to be accessed as numpy.random.rand(). Or use the rand() from the matlib module. But the "numpythonic" way is to use numpy.random.random(), which takes a tuple for the shape, like other numpy functions.

Table of Rough MATLAB-NumPy Equivalents

The table below gives rough equivalents for some common MATLAB® expressions. These are not exact equivalents, but rather should be taken as hints to get you going in the right direction. For more detail read the built-in documentation on the NumPy functions.

Some care is necessary when writing functions that take arrays or matrices as arguments --- if you are expecting an array and are given a matrix, or vice versa, then '*' (multiplication) will give you unexpected results. You can convert back and forth between arrays and matrices using

asarray: always returns an object of type array

asmatrix or mat: always return an object of type matrix

asanyarray: always returns an array object or a subclass derived from it, depending on the input. For instance if you pass in a matrix it returns a matrix.

These functions all accept both arrays and matrices (among other things like Python lists), and thus are useful when writing functions that should accept any array-like object.

In the table below, it is assumed that you have executed the following commands in Python:

fromnumpyimport*importscipyasSciimportscipy.linalg

Also assume below that if the Notes talk about "matrix" that the arguments are rank 2 entities.

THIS IS AN EVOLVING WIKI DOCUMENT. If you find an error, or can fill in an empty box, please fix it! If there's something you'd like to see added, just add it.

cholesky factorization of a matrix (chol(a) in matlab returns an upper triangular matrix, but linalg.cholesky(a) returns a lower triangular matrix)

[V,D]=eig(a)

D,V = linalg.eig(a)

eigenvalues and eigenvectors of a

[V,D]=eig(a,b)

V,D = Sci.linalg.eig(a,b)

eigenvalues and eigenvectors of a,b

[V,D]=eigs(a,k)

find the k largest eigenvalues and eigenvectors of a

[Q,R,P]=qr(a,0)

Q,R = Sci.linalg.qr(a)

mat(...)

QR decomposition

[L,U,P]=lu(a)

L,U = Sci.linalg.lu(a) or LU,P=Sci.linalg.lu_factor(a)

mat(...)

LU decomposition (note: P(Matlab) == transpose(P(numpy)) )

conjgrad

Sci.linalg.cg

mat(...)

Conjugate gradients solver

fft(a)

fft(a)

mat(...)

Fourier transform of a

ifft(a)

ifft(a)

mat(...)

inverse Fourier transform of a

sort(a)

sort(a) or a.sort()

mat(...)

sort the matrix

[b,I] = sortrows(a,i)

I = argsort(a[:,i]), b=a[I,:]

sort the rows of the matrix

regress(y,X)

linalg.lstsq(X,y)

multilinear regression

decimate(x, q)

Sci.signal.resample(x, len(x)/q)

downsample with low-pass filtering

unique(a)

unique(a)

squeeze(a)

a.squeeze()

Notes

Submatrix: Assignment to a submatrix can be done with lists of indexes using the ix_ command. E.g., for 2d array a, one might do: ind=[1,3]; a[np.ix_(ind,ind)]+=100.

HELP: There is no direct equivalent of MATLAB's which command, but the commands help and source will usually list the filename where the function is located. Python also has an inspect module (do import inspect) which provides a getfile that often works.

INDEXING: MATLAB® uses one based indexing, so the initial element of a sequence has index 1. Python uses zero based indexing, so the initial element of a sequence has index 0. Confusion and flamewars arise because each has advantages and disadvantages. One based indexing is consistent with common human language usage, where the "first" element of a sequence has index 1. Zero based indexing simplifies indexing. See also a text by prof.dr. Edsger W. Dijkstra.

RANGES: In MATLAB®, 0:5 can be used as both a range literal and a 'slice' index (inside parentheses); however, in Python, constructs like 0:5 can only be used as a slice index (inside square brackets). Thus the somewhat quirky r_ object was created to allow numpy to have a similarly terse range construction mechanism. Note that r_ is not called like a function or a constructor, but rather indexed using square brackets, which allows the use of Python's slice syntax in the arguments.

LOGICOPS: & or | in Numpy is bitwise AND/OR, while in Matlab & and | are logical AND/OR. The difference should be clear to anyone with significant programming experience. The two can appear to work the same, but there are important differences. If you would have used Matlab's & or | operators, you should use the Numpy ufuncs logical_and/logical_or. The notable differences between Matlab's and Numpy's & and | operators are:

Non-logical {0,1} inputs: Numpy's output is the bitwise AND of the inputs. Matlab treats any non-zero value as 1 and returns the logical AND. For example (3 & 4) in Numpy is 0, while in Matlab both 3 and 4 are considered logical true and (3 & 4) returns 1.

Precedence: Numpy's & operator is higher precedence than logical operators like < and >; Matlab's is the reverse.

If you know you have boolean arguments, you can get away with using Numpy's bitwise operators, but be careful with parentheses, like this: z = (x > 1) & (x < 2). The absence of Numpy operator forms of logical_and and logical_or is an unfortunate consequence of Python's design.

RESHAPE and LINEAR INDEXING: Matlab always allows multi-dimensional arrays to be accessed using scalar or linear indices, Numpy does not. Linear indices are common in Matlab programs, e.g. find() on a matrix returns them, whereas Numpy's find behaves differently. When converting Matlab code it might be necessary to first reshape a matrix to a linear sequence, perform some indexing operations and then reshape back. As reshape (usually) produces views onto the same storage, it should be possible to do this fairly efficiently. Note that the scan order used by reshape in Numpy defaults to the 'C' order, whereas Matlab uses the Fortran order. If you are simply converting to a linear sequence and back this doesn't matter. But if you are converting reshapes from Matlab code which relies on the scan order, then this Matlab code: z = reshape(x,3,4); should become z = x.reshape(3,4,order='F').copy() in Numpy.

Customizing Your Environment

In MATLAB® the main tool available to you for customizing the environment is to modify the search path with the locations of your favorite functions. You can put such customizations into a startup script that MATLAB will run on startup.

NumPy, or rather Python, has similar facilities.

To modify your Python search path to include the locations of your own modules, define the PYTHONPATH environment variable.

To have a particular script file executed when the interactive Python interpreter is started, define the PYTHONSTARTUP environment variable to contain the name of your startup script.

Unlike MATLAB®, where anything on your path can be called immediately, with Python you need to first do an 'import' statement to make functions in a particular file accessible.

For example you might make a startup script that looks like this (Note: this is just an example, not a statement of "best practices"):

# Make all numpy available via shorter 'num' prefiximportnumpyasnum# Make all matlib functions accessible at the top level via M.func()importnumpy.matlibasM# Make some matlib functions accessible directly at the top level via, e.g. rand(3,3)fromnumpy.matlibimportrand,zeros,ones,empty,eye# Define a Hermitian functiondefhermitian(A,**kwargs):returnnum.transpose(A,**kwargs).conj()# Make some shorcuts for transpose,hermitian:# num.transpose(A) --> T(A)# hermitian(A) --> H(A)T=num.transposeH=hermitian

MATLAB packages/tools and equivalent for use with NumPy

Symbolic calculation: swiginac appears to be the most complete current option. sympy is a project aiming at bringing the basic symbolic calculus functionalities to Python. Also to be noted is PyDSTool which provides some basic symbolic functionality.

Eclipse: is one nice option for python code editing via the pydev plugin.

Wing IDE: a commercial IDE available for multiple platforms. The professional version has an interactive debugging prompt similar to MATLAB's.

Python(x,y) scientific and engineering development software for numerical computations, data analysis and data visualization. The installation includes, among others, Spyder, Eclipse and a lot of relevant Python modules for scientific computing.